Decomposing temporal changes of biodiversity to loss, survival, and recruitment of individuals: analysis of the North-American avifauna

.title[
# Decomposing temporal changes of biodiversity to loss, survival, and recruitment of individuals: analysis of the North-American avifauna
]
.author[
### <br><br><br><br>François Leroy<br>Marta Jarzyna<br>Petr Keil
]
.institute[
### <br><br><br><br><br>Czech University of Life Sciences<br>Prague
]

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# Biodiversity

* Multi-faceted (species richness, turnover, abundance)

* Changes through time

* Perturbed (mostly) by human activities

<br>

* the best metric to follow biodiversity state

* overall decline of 69% (*acc.* Living Planet Index)

.center[
`$\Rightarrow$` Marine Sharks and Rays: -71%<br><br>
`$\Rightarrow$` Freshwater: -83%<br><br>
`$\Rightarrow$` -3 billion North-American birds since 70's
]

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# Decomposing abundance change

* Temporal change of abundance ( `$\Delta N$` ) results of `$3$` processes

.center[
<img src="data:image/png;base64,#images/deltaN_concept1.png" width="100%" />
]
<br>
`$$\Rightarrow \Delta N = N_{t1} - N_{t0} = R - L$$`

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# Decomposing growth rate

* Growth rate: per individual average change

<br>

* Loss rate = individual probability of dying/emigrating

* Loss rate `$= \frac{L}{N_{t0}}$`

]

* Recruitment rate = individual probability of producing an individual

* Recruitment rate `$= \frac{R}{N_{t0}}$`

]

`$\Rightarrow$` Growth rate = `$\frac{\Delta N}{N_{t0}} = \frac{R}{N_{t0}} - \frac{L}{N_{t0}}$`

]

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## Problem

Assessing the ongoing decrease of abundance does not tell us which process is driving the trend

### Increase in recruitment?
Better reproductive success, better breeding habitat...

#### Or

### Decrease of individual loss?
Reduction of threats, better habitat quality...

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# Data - Breeding Bird Survey (BBS)

* Structured data on North American avifauna

* From 1987 to 2021

]

* More than 1000 routes

* 564 species

]

]

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# Model - Dail & Madsen

* Bayesian hierarchical model

`$$N_{t+1} = Survival_{t+1} + Recruitment_{t+1}$$`
.center[

#### with

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`$$Survival_{t+1} \sim Bin(N_t, \omega)$$`

`$$Recruitment_{t+1} \sim Poisson(\gamma)$$`
.footnote[
**Note:** `$Loss_t = N_t - S_{t+1}$`
]

<br>

* Accounting for detection probabilities, depending on meteorological covariates:

<br>

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## We assessed

###  1) temporal change of abundance ( `$\Delta N$` ), recruitment ( `$\Delta R$` ) and loss ( `$\Delta L$` ) from 1987 and 2021 all across North America

### 2) temporal change of growth rate ( `$\Delta N_r$` ), recruitment rate ( `$\Delta R_r$` ) and loss rate ( `$\Delta L_r$` )

### 3) which process, between recruitment (rate) and loss (rate), is driving the temporal change of abundance

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# Change in abundance, recruitment and loss

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# Change in abundance, recruitment and loss
  
.center[
<img src="data:image/png;base64,#images/map_rec.jpg" width="100%" />
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# Change in abundance, recruitment and loss
  
.center[
<img src="data:image/png;base64,#images/map_loss.jpg" width="100%" />
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# Change in abundance, recruitment and loss
  
.center[
<img src="data:image/png;base64,#images/map_all_number.jpg" width="90%" />
]

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss: BBS routes

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# Recruitment vs. Loss in space

<img src="data:image/png;base64,#images/map_recVsLoss.png" width="90%" />
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# Recruitment vs. Loss in space (smoothened)

<img src="data:image/png;base64,#images/map_recVsLoss_gam.png" width="90%" />
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# Change in growth, recruitment and loss rates

<img src="data:image/png;base64,#images/map_gr.png" width="100%" />
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# Change in growth, recruitment and loss rates

<img src="data:image/png;base64,#images/map_recRate.png" width="90%" />
]

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# Change in growth, recruitment and loss rates

<img src="data:image/png;base64,#images/map_lossRate.png" width="90%" />
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# Change in growth, recruitment and loss rates

<img src="data:image/png;base64,#images/map_rates_all.png" width="90%" />
]

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